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VOL. 7 | 2006 New Integrable Multi-Component NLS Type Equations on Symmetric Spaces: $\mathbb{Z}_4$ and $\mathbb{Z}_6$ Reductions
Georgi G. Grahovski, Vladimir S. Gerdjikov, Nikolay A. Kostov, Victor A. Atanasov

Editor(s) Ivaïlo M. Mladenov, Manuel de León


The reductions of the multi-component nonlinear Schrödinger models related to C.I and D.III type symmetric spaces are studied. We pay special attention to the MNLS related to the $\mathfrak{sp}(4)$, $\mathfrak{so}(10)$ and $\mathfrak{so}(12)$ Lie algebras. The MNLS related to $\mathfrak{sp}(4)$ is a three-component MNLS which finds applications to Bose–Einstein condensates. The MNLS related to $\mathfrak{so}(12)$ and $\mathfrak{so}(10)$ Lie algebras after convenient $\mathfrak{Z}_6$ or $\mathfrak{Z}_4$ reductions reduce to three and four-component MNLS showing new types of $\chi(3)$-interactions that are integrable. We briefly explain how these new types of MNLS can be integrated by the inverse scattering method. The spectral properties of the Lax operators $L$ and the corresponding recursion operator $\Lambda$ are outlined. Applications to spinor model of Bose–Einstein condensates are discussed.


Published: 1 January 2006
First available in Project Euclid: 13 July 2015

zbMATH: 1101.35070
MathSciNet: MR2228370

Digital Object Identifier: 10.7546/giq-7-2006-154-175

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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